Frank had already noticed the people - a number of them had ricocheted off his back when he stopped to take in the view: an immense air-conditioned atrium five stories high filled with gleaming shops, its bubble elevators and escalators packed with Singaporeans doing their Christmas shopping.

Some of the shoppers were probably heading for the metro department store, where silver-suited shop assistants staff a computer that will help you pick your ideal gift for friend, lover, or enemy.

Computers are big this Christmas. A variety of home models are selling well. So is a kids' computer: ''Something your boy can practice on before he gets his Apple,'' a shop assistant explained.

And of course the old Singapore standbys - videos and designer clothes - are selling as well as usual.

Somehow this wasn't how Frank and his wife imagined Singapore when they planned their Far East tour.

What had they heard about Singapore before they came? ''Well, the Raffles,'' Frank's wife said, referring to the city's famous old colonial hotel, now slightly past its prime. Most tourists who come here from outside Southeast Asia are probably equally surprised: Instead of a quiet old colonial seaport they find a brash, modern, well-scrubbed, and highly successful island.

It's a tiny place - its population the size of Brooklyn, its land area that of Chicago.

And its annual average income - about $5,000 in US dollars - is so high that it has difficulty persuading some financial institutions that it should be considered a developing country.

Singapore Prime Minister Lee Kuan Yew and his senior ministers started off their political lives as socialists. ''But over the years,'' an official said, ''ideological considerations have given way to more important ones - national survival.''

Survival is still a key issue as far as Lee Kuan Yew is concerned. The Kampuchea (Cambodia) question and growing Soviet influence in the region underline the area's potential for political instability.

The world recession - which has affected Singapore but perhaps less than expected - reminds the leadership that the island, which has no natural resources, is particularly vulnerable to fluctuations in the global economy.

Most important, Singapore's leaders see their island moving into trouble. Many of its people do not share the leadership's sense of foreboding. One of Lee Kuan Yew's nightmares seems to be that, as he put it recently, ''in a fit of pique or a moment of madness,'' Singaporeans might vote for the ''politics of opposition for the sake of opposition,'' and bring the country to its knees.

Another key problem is that Singapore has to face the future without the reserves of talent it could call on a generation ago.

Only two in Lee's first Cabinet - one of them Lee - were Singapore-born. The others, and most of the top planners and administrators who developed the island , came from Malaysia, China, India in colonial times.

Without the non-Singaporeans, Lee wrote recently, ''Singapore's performance would not have been half as good.'' But in the coming years the talent pool will be shallower: With his normal cool precision, Lee says he has calculated that between 12 and 14 ''talented and balanced'' Singaporeans capable of top leadership will be born every year.

And things will get worse, Lee adds, because well-educated Singaporeans - who , Lee says, are more likely to produce bright offspring - are having smaller families than less-educated citizens.

One response to the problem has been to encourage immigration of gifted foreigners to teach in universities and take senior administrative jobs. Though still limited, this has produced some discontent among Singaporeans.

Another has been to make Singaporean salaries attractive by any standards. Recently, for example, the Army improved its pay to attract better caliber officers. The result: A major general can earn up to $86,000 a year. And recent changes in the constitution of the ruling People's Action Party (PAP) gave rise to speculation that Singapore was heading for a one-party state. The government denies this, but, as it moves ahead into an uncertain world, it will probably want to keep its options open.